Analysis On Earth-sheltered Dwellings’ Reliability Based On Response Surface Method

Earth-sheltered dwellings refers to the original soil by artificial digging that is cave living form, which has a history of thousands of years. Earth-sheltered dwellings habitat from the natural and is harmony with nature, which make full use of underground heat and soil, "warm in winter and cool in summer", with thermal insulation, heat insulation, energy storage, regulating cavern microclimate function, and which is the most consistent with ecological principles. Earth-sheltered dwellings are entirely by digging raw earth forming arch self supporting system without support; construction is without design, and is the lack of scientific computing, whose construction technology relies mostly on local craftsman’s experience and spread and evolution in oral teaching, rare in the text; this building can live for hundreds of years. The ecological construction of this "low cost, low energy consumption, low pollution, long life" has aroused extensive interest of scholars home and abroad. The thoughts of ecology, construction experience, the specific cultural tradition, ingenious and construction technology are wisdom and wealth our ancestors left, which has the value of preservation and inheritance. Researching the reliability of earth-sheltered dwellings is important way to uncover the traditional kiln habitat and existence rationality; research results will provide the basis for the safety assessment and modernization of the residential structure, provide technical supporting for the reinforcement and repair in the service of cave dwelling.Existing methods of reliability analysis are diverse, there is first order second moment method, quadratic order second moment method, monte carlo method and response surface method, etc., when functions for implicit or unknown, only the monte carlo method and response surface method is available.There is no relevant regulations and standards of earth-sheltered dwelling in the limit state of regulation, so its function is unknown, which can only use the monte carlo method and response surface method;Such as the monte carlo method is adopted to solve the reliability, means to establish finite element model of the tens of millions which cannot be achieved;So, the response surface method is the only feasible approach for the analysis of earth-sheltered dwellings’ reliability.The process of building response surface method for earth-sheltered dwellings are as follows: ①combined with the cusp catastrophic model and finite element strength subtraction, determine the bearing capacity limit state of earth-sheltered dwellings, with "five steps" to establish a reasonable finite element model, using displacement or plastic dissipation cusp catastrophic model, shear strength security reserve can be obtained; ② Determine the the "input" and "output" of response surface, "input" are the random variable, "output" is shear strength security reserve minus the basic safety factor of safety; ③Choosing the form of Response surface: comparing the reliability result of quadratic polynomial response surface and RBF response surface, the result is close and within the error range, so two method are all right. The quadratic polynomial response surface can get random variables’ sensitivity factor, and can be extended to the generalized random space to deal with the reliability of the related random variables, so quadratic polynomial response surface is the first choice; ④The choose of different combinations of random variables to all cave density and a typical dwelling in Shan city, Henan province, which can be referred to the "standard deviation interval gradient" method proposed in this paper. Then the quadratic polynomial response surface method can be used, repeating the first and second step, until the response surface convergent, reliability problem can be solved. In the solving process of reliability problem, improving the varied f sequence response surface method to fij sequence response surface method, the fy is different in every circulation of finite element calculation and to every random variable, to ensure that the geometric parameters are positive. ⑤Considering correlated parameters, the quadratic polynomial response surface method is extended to the generalized random space; Considering the fuzziness of material parameters, the fuzzy random problem is converted to random problem in interval with a-cuts; Considering the fuzziness of failure criterion, the fuzzy failure criterion is set, and the problem of random fuzzy is converted to stochastic problem with the membership function. In addition, this paper probes into the influence of heavy rainfall and earthquake on reliability.Through the earth-sheltered dwellings’ reliability analysis(for example in Shan city, Henan province), the following conclusions can be get: ①Earth-sheltered dwellings’ reliability is high; The geometry size is chosen reasonably without scientific calculation:the cave span and cave leg width are positive correlated, with the increasing of cave span, the cave leg width will increase accordingly, so the safety does not reduce, which verifies rationality of the construction experience. The cave span’s discreteness is small, which satisfy the security and ensure enough living space. ②"Standard deviation interval gradient method"proposed in this paper can determine which random variable’s influence on reliability index is larger in front of the reliability analysis, and the results are consistent with the sensitivity factor order after reliability analysis, so this method is correct. The method can provide reference for building and reinforcing cave dwellings. Because the cohesive force and the cave leg width of loess are key random variables, and vertical displacement on the top of the cave is the largest, so when building new caves, the loess with high cohesive force should be chosen, and ensure that the cave leg width is large enough. For the reinforcement and reconstruction of cave dwellings, the cave top shoulder be supported and the cave leg should be reinforced. ③When the reliability of cave dwellings in a region is evaluated, the positive correlation between cave leg width and span should be considered or not according to the actual situation, and the result is conservative without considering the correlation; Because it’s difficult to obtain the negative correlation coefficient between cohesive force and angle of internal friction by experiment, and the reliable index will increase when the correlation is considered, so the correlation will be not considered which is a safety reserve. Indirect considering fuzzy factors, the reliability analysis of benchmark safety coefficient is 1.1, rather than considering fuzzy factors of 1.0, compared with considering fuzzy factors reliability index declined, the results are conservative. ④After heavy rainfall or earthquake, the earth-sheltered dwellings can still be used normally. After heavy rainfall, only a small scope underground loess’s saturation is big, the displacement and stress increase of cave dwellings are small. When the geometric parameters and material parameters are average value, no matter frequent earthquake or rarely met earthquake, there will be no plastic deformation area, which shows that after the earthquake, the cave dwellings whose parameters above the average can be used normally. Under earthquake cases, the cave leg is still a key part of the cave dwellings in stability, no matter frequent earthquake or rarely met earthquake, damage is the result of the cave leg’s plastic zone development constantly.